Muhammad's Dissection

Geometry Level 3

Let \( A_1B_1C_1D_1A_2B_2C_2D_2 \) be a unit cube, where the vertex \(X_2\) is vertically above the vertex \(X_1\). Let \( M \) be the center of face \( A_2 B_2 C_2 D_2 \). Rectangular pyramid \( MA_1B_1C_1D_1 \) is cut out of the cube. The surface area of the solid that remains after the pyramid is removed is expressed in the form \( a + \sqrt{b} \), where \( a \) and \( b \) are positive integers and \( b \) is not divisible by the square of any prime. What is \( a+b \)?

This problem is posed by Muhammad A.

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